Problem: $\begin{cases} g(1)=51 \\\\ g(n)=g(n-1)+2 \end{cases}$ Find an explicit formula for $g(n)$. $g(n)=$
Answer: From the recursive formula, we can tell that the first term of the sequence is ${51}$ and the common difference is ${2}$. This is the explicit formula of the sequence: $g(n)={51} +{2}(n-1)$ Note that this solution strategy results in this formula, however an equally correct solution can be written in other equivalent forms as well.